A 45-degree slope is a 100 percent grade, and a vertical wall is infinite
Grade is usually quoted as rise over run times 100, which leads to a quirk: a 45-degree hill is a 100 percent grade, and as the slope nears vertical the percentage races toward infinity. Measure along the slope instead, and the same 45-degree hill comes out at 71 percent.
Grade, gradient, pitch and incline all describe tilt, normally as vertical rise divided by horizontal run. Europe and the US mostly use percentages, and European road signs display them. European railways often prefer per-mille figures, while Britain and Australia give rail grades as 1 in n, so a line climbing 5 feet in every 1,000 is 1 in 200; British roads used that style until the 1970s. With those ratios, confusingly, a bigger number means a gentler slope. Designers like round figures, so the notation chosen can even influence which gradients get built.
Railways care intensely because the steepest stretch of a line caps the load a locomotive can pull; hauling a heavy train at 20 km/h up a 1 percent slope can take ten times the force needed on the level. Early British engines and their brakes were so feeble that the Great Western main line was laid at gradients as gentle as 1 in 1,320, earning the nickname Brunel's Billiard Table. Steep sections were bunched into short runs such as Euston to Camden Town, where extra engines or cables could help.
Beyond a certain point, machinery takes over. Switzerland's Pilatus Railway, regarded as the steepest rack railway, reaches 48 percent, and the Scenic Railway at Katoomba in Australia, claimed as the steepest passenger funicular, hits 122 percent, or 52 degrees. On US federally funded highways, grades up to 6 percent are generally allowed in mountainous and hilly urban areas.
City streets can be wilder. Guinness lists Baldwin Street in Dunedin, New Zealand, as the steepest in the world at 34.8 percent, after an appeal overturned a ruling that had briefly given the title to Ffordd Pen Llech in Harlech, Wales. Yet San Francisco has ten public blocks steeper than 30 percent, topped by a stretch of Bradford Street at 41 percent, and one of its bus routes climbs a 23.1 percent grade.
Source: Grade (slope)
